Finite Math Examples

$0.5 s + 0.5 s^{2}$ , $0.6 s + 0.4 s^{2}$

Step 1

Divide the higher order polynomial by the other polynomial in order to find the remainder.

$\frac{0.5 s + 0.5 s^{2}}{0.6 s + 0.4 s^{2}}$

Step 2

Reorder $0.5 s$ and $0.5 s^{2}$ .

$\frac{0.5 s^{2} + 0.5 s}{0.6 s + 0.4 s^{2}}$

Step 3

Reorder $0.6 s$ and $0.4 s^{2}$ .

$\frac{0.5 s^{2} + 0.5 s}{0.4 s^{2} + 0.6 s}$

Step 4

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of $0$ .

$0.4 s^{2}$

$0.6 s$

$0$

$0.5 s^{2}$

$0.5 s$

$0$

Step 5

Divide the highest order term in the dividend $0.5 s^{2}$ by the highest order term in divisor $0.4 s^{2}$ .

							$1.25$
	$0.4 s^{2}$	+	$0.6 s$	+	$0$		$0.5 s^{2}$	+	$0.5 s$	+	$0$

Step 6

Multiply the new quotient term by the divisor.

Step 7

The expression needs to be subtracted from the dividend, so change all the signs in $0.5 s^{2} + 0.75 s + 0$

Step 8

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

Step 9

The final answer is the quotient plus the remainder over the divisor.

$1.25 + \frac{- 0.25 s}{0.4 s^{2} + 0.6 s}$

Step 10

The remainder is the part of the answer that is left after the division by $0.6 s + 0.4 s^{2}$ is complete.

$- 0.25 s$